p.252, icon at Example 2 #1. Certain rules allow us to determine by inspection when a positive integer n is divisible by a positive integer k. For example, 5❘n if and only if n ends in the digit 5 or 0. Similarly, 2❘n if and only if n ends in one of the digits 0, 2, 4, 6, 8. There is also a rule to determine divisibility by 3: 3❘n if and only if the sum of the digits in n is divisible by 3. For example 3 | 478, 125 because the sum of the six digits in 478, 125 is 27, which is divisible by 3. Why does the rule work?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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p.252, icon at Example 2
#1. Certain rules allow us to determine by inspection when a positive integer n is divisible by a positive integer k.
For example, 5❘n if and only if n ends in the digit 5 or 0. Similarly, 2❘n if and only if n ends in one of the digits
0, 2, 4, 6, 8.
There is also a rule to determine divisibility by 3:
3❘n if and only if the sum of the digits in n is divisible by 3.
For example 3 | 478, 125 because the sum of the six digits in 478, 125 is 27, which is divisible by 3. Why does the rule
work?
Transcribed Image Text:p.252, icon at Example 2 #1. Certain rules allow us to determine by inspection when a positive integer n is divisible by a positive integer k. For example, 5❘n if and only if n ends in the digit 5 or 0. Similarly, 2❘n if and only if n ends in one of the digits 0, 2, 4, 6, 8. There is also a rule to determine divisibility by 3: 3❘n if and only if the sum of the digits in n is divisible by 3. For example 3 | 478, 125 because the sum of the six digits in 478, 125 is 27, which is divisible by 3. Why does the rule work?
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